Frequency-domain interpolation for simultaneous periodic nonuniform samples
Marco A. Gurrola-Navarro · 2018
We present a frequency-domain numerical procedure to interpolate n-1 points per sampling period of a nonuniform periodic set of samples. The samples are acquired from a continuous time band-limited input signal at a rate n times smaller than the Nyquist rate. No information is lost because, at every sample period, n-1 additional values are simultaneously sampled from an equal number of filtered versions of the input signal. The filters are a set of different linear systems previously selected to be implemented with simple electrical networks. A difference with previous presented works is that we do not recover the continuous input signal, but a sampled version of the input signal that satisfies the Nyquist rate. For this, we apply the fast Fourier transform to the n sample series and eliminate the aliasing in the spectra point by point. We accomplish this using a priori knowledge of the selected filters to establish and numerically solve a set of linear equation systems. Once we have recovered the complete discrete spectrum of the input signal, we apply the inverse fast Fourier transform to recover the discrete time version of this signal. The theoretical basis of the proposed approach is presented and it is corroborated with a numerical example.